Sports field calibration is critical for mapping image coordinates to standardized coordinates, enabling precise analysis of player trajectories and tactical formations. However, traditional methods designed for TV broadcast footage rely on sparse field features (corners, lines) that are susceptible to occlusion and viewpoint variations, limiting their effectiveness for tactical camera calibration. To address these limitations, we propose a novel pose-based calibration framework that directly regresses the 6-DoF camera pose from tactical view images. The proposed framework consists of three novel components: (1) a Lanczos-based spatial encoding module that preserves fine-grained geometric structures in the field representation, (2) an offset-guided sub-pixel localization strategy that enhances occlusion robustness by refining keypoints’ position to accuracy, and (3) a query-driven pose regression with attention mechanisms that directly estimates camera pose without requiring additional calibration metadata. Extensive experiments on the SoccerNet-2023 and World Cup 2014 benchmarks demonstrate that our method achieves state-of-the-art performance in Jacobian consistent accuracy (JaC@t), establishing higher accuracy and cross-dataset generalization capabilities.

Abstract Process task duration data often exhibit multiple peaks, indicating differences in, for example, customer ages and preferences, resource capabilities or the day/hour of a week. This heterogeneous data, which captures diverse customer patterns, should be represented using different models, resulting in an overall mixture model. This paper introduces gamma mixture models to represent various customer patterns in task duration data, with a focus on automating the fitting process. The approach involves a two-stage procedure: first, divide-and-conquer using peak-, equidistance- and cluster-based techniques to partition data, and automatically fit gamma distributions to each subset. The second stage then improves the fitted mixture model by directly searching the log-likelihood surface. The method is compared with the expectation–maximization (EM) algorithm and an open tool (HyperStar), using both artificially generated datasets and a publicly available hospital billing dataset, demonstrating its effectiveness and time efficiency in modelling heterogeneous process duration data. Furthermore, a case study on process conformance checking is conducted using the hospital billing dataset, highlighting a potential application area for the method in process mining.

Within the realm of business context, process duration signifies time spent by customers between successive activities. This temporal perspective offers important insight to customer behavior, highlighting potential bottlenecks, and influencing business management decisions. The distribution of these process duration often changes over time due to factors such as seasonality, emerging legislation, changes to supply chains, and customer demand. Referred to as concept drift, these variations pose challenges for robust process modeling, understanding, and refinement. Subsequently, gamma mixture models are widely employed to model durations. These source data can, however, become left-truncated and right-censored within any specific observation window thereby necessitating a (well-known) modification to the likelihood function. The approach reported in this article leveraged this adapted likelihood across a series of observation windows, applying the likelihood ratio test to identify duration changes/concept drift. Due to its flexibility in modelling any duration distribution, the gamma mixture model was used with Nelder–Mead optimized likelihood for the left-truncated and right-censored data. The number of gamma components was determined by the Bayesian information criterion. The proposed framework underwent validation through simulated exponential samples, leading to recommendations for its practical application. Subsequently, we applied the methodology to three real-life event logs exhibiting diverse characteristics. Experimental results showcase the effectiveness of our approach in terms of data fitting, as compared to Kaplan–Meier curves, and in detecting instances of drift. This comprehensive validation underscores the practical utility and reliability of our framework for dynamic business scenarios.

Over-sampling technology for handling the class imbalanced problem generates more minority samples to balance the dataset size of different classes. However, sampling in original data space is ineffective as the data in different classes is overlapped or disjunct. Based on this, a new minority sample is presented in terms of the manifold distance rather than Euclidean distance. The overlapped majority and minority samples apt to distribute in fully disjunct subspaces from the view of manifold learning. Moreover, it can avoid generating samples between the minority data locating far away in manifold space. Experiments on 23 UCI datasets show that the proposed method has the better classification accuracy.